Mid-Term Study Guide A2

Front

What is the equation of the graph y = |x - 1| + 7 when reflected across the y-axis?

Back

y = |x + 1| + 7

Front

Simplify the expression (−6x^3 − 4x^2 − 8) + (x^3 − x^2 − 9x + 4).

Back

-5x^3 + 5x^2 - 9x - 4

Front

What is the range of a function that has a minimum value of -4 and approaches but does not include 2?

Back

[-4, 2)

Front

How do you solve the equation x² + x = 12?

Back

Rearrange to x² + x - 12 = 0, then factor to (x - 3)(x + 4) = 0, giving x = 3 and x = -4.

Front

What is the definition of a function's range?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a graph to be reflected across the y-axis?

Back

Reflecting a graph across the y-axis means that for every point (x, y) on the graph, there is a corresponding point (-x, y).

Front

What is the process for simplifying polynomial expressions?

Back

Combine like terms by adding or subtracting coefficients of terms with the same degree.

Front

What is the vertex form of a quadratic function?

Back

The vertex form is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.

Front

What is the significance of the absolute value in the equation y = |x - 1| + 7?

Back

The absolute value indicates that the output will always be non-negative, creating a V-shaped graph.

Front

How do you determine the x-intercepts of a quadratic function?

Back

Set the function equal to zero and solve for x using factoring, completing the square, or the quadratic formula.